What is the median of the following sale prices: $195,000, $210,000, $185,000, $225,000, and $200,000?
Correct Answer
A) $200,000
First arrange in order: $185,000, $195,000, $200,000, $210,000, $225,000. The median is the middle value, which is $200,000.
Why This Is the Correct Answer
Option A ($200,000) is correct because when the five sale prices are arranged in ascending order ($185,000, $195,000, $200,000, $210,000, $225,000), the median is the middle (third) value. With an odd number of data points (5 values), the median is simply the value that falls exactly in the center position. Since $200,000 occupies the third position out of five values, it represents the true median of this dataset.
Why the Other Options Are Wrong
Option B: $203,000
Option B ($203,000) is incorrect because it represents the arithmetic mean (average) of the five values, not the median. This is calculated by adding all values ($1,015,000) and dividing by the number of values (5), which equals $203,000. Students often confuse mean and median, but they are distinctly different measures of central tendency.
Option C: $210,000
Option C ($210,000) is incorrect because it represents the fourth value in the ordered dataset, not the middle value. While $210,000 is one of the actual sale prices, it falls above the median position and would only be relevant if we were looking for the third quartile or if this were an even-numbered dataset requiring averaging.
Option D: $195,000
Option D ($195,000) is incorrect because it represents the second value in the ordered dataset, falling below the true median position. Although $195,000 is an actual sale price from the dataset, it's positioned too low in the ordered sequence to be the median value.
SORT-SPOT-SELECT Method
SORT the values in order, SPOT the middle position, SELECT that value. For odd numbers, it's the exact middle; for even numbers, average the two middle values. Remember: 'Median = Middle, Mean = Mathematical average.'
How to use: When you see a median question, immediately write 'SORT-SPOT-SELECT' at the top of your scratch work, then follow each step systematically. Count the total values to determine if odd (pick middle) or even (average two middle values).
Exam Tip
Always arrange the numbers in order first - don't try to find the median from unsorted data. Double-check your count to ensure you've identified the correct middle position, and verify your answer by confirming equal numbers of values above and below your median.
Common Mistakes to Avoid
- -Calculating the mean (average) instead of the median
- -Forgetting to sort the data in numerical order before finding the middle value
- -Miscounting the position of the middle value in the ordered dataset
Concept Deep Dive
Analysis
This question tests the fundamental statistical concept of median, which is a critical measure of central tendency used extensively in real estate appraisal. The median represents the middle value in a dataset when arranged in ascending or descending order, making it particularly valuable in real estate because it's less affected by extreme values (outliers) than the mean. In appraisal practice, median values help appraisers understand typical market conditions and identify reasonable price ranges for comparable sales. Understanding how to calculate and interpret median values is essential for market analysis, comparable sales selection, and supporting valuation conclusions.
Background Knowledge
The median is a measure of central tendency that identifies the middle value in an ordered dataset, making it particularly useful in real estate analysis because it's not skewed by extremely high or low sale prices. For datasets with an odd number of values, the median is the middle value; for even-numbered datasets, it's the average of the two middle values.
Real-World Application
Appraisers use median sale prices to analyze market trends and establish value ranges for properties. When preparing a market analysis, the median helps identify typical selling prices while filtering out the influence of luxury sales or distressed properties that might skew the average price.
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